A139715 G.f. A(x) satisfies: A(x) = G(G(x)) where G(x) = x - A(x)^2 = g.f. of A139702.

1, -2, 10, -69, 568, -5250, 52792, -566830, 6420640, -76095972, 938077528, -11975951312, 157808048792, -2140767942096, 29835756120952, -426490803168368, 6244476409802008, -93541594534237356, 1432261132629484052, -22397290780155132728

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

Series_Reversion(A(x)) = F(F(x)) = F(x) + x^2 where F(x) = g.f. of A138740.

Example

A(x) = x - 2*x^2 + 10*x^3 - 69*x^4 + 568*x^5 - 5250*x^6 + 52792*x^7 -+...
Let G(x) = x - A(x)^2 = g.f. of A139702:
G(x) = x - x^2 + 4*x^3 - 24*x^4 + 178*x^5 - 1512*x^6 + 14152*x^7 -+...
then A(x) = G(G(x)).

Prog

(PARI) {a(n)=local(A=x); if(n<1, 0, for(i=1, n, A=serreverse(x + (A+x*O(x^n))^2)); polcoeff(subst(A, x, A+x*O(x^n)), n))}

Crossrefs

Cf. A139702, A138740.

Sequence in context: A056755 A123617 A325054 * A293914 A259114 A051575

Adjacent sequences: A139712 A139713 A139714 * A139716 A139717 A139718

Keyword

sign

Author

Paul D. Hanna, Apr 30 2008

Status

approved